Using Finite Element Results for Fatigue Analysis

F.A. Conle, Univ. of Waterloo, Nov. 8 2010.

Educational Background Article
http://fde.uwaterloo.ca/Fde/Notches.new/feaFatigue.html
Copyright (C) 2010 F.A. Conle and Univ. of Waterloo
Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.3
or any later version published by the Free Software Foundation;
with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
A copy of the license is available here: "GNU Free Documentation License".
( "http://www.gnu.org/licenses/fdl.html" )

Introduction:

The use of Finite Element Analysis (FEA) results to calculate durability
was a topic of research in the 1970s (e.g.:Ref.[1] ), and since then has become
a proven method used by ground vehicle industry
engineers to predict fatigue life of components and structures. In 1982 Landgraf[2]
was one of the first to bring together the concepts of the "local stress-strain",
which recognized the elastic+plastic behavior of cyclic deformation, with the
elastic stress calculation from FEA.

The combined method uses elastic stress calculations (often von Mises equivalent
stress), for each element of some large component load placed on the FEA model,
to proportionally scale a variable amplitude load history
into a elastic element stress history. The load histories at that time consisted
of exceedence[3] or Rainflow[4-6] counted histograms, rather than the
actual time series sequences of load or stress.

Elastic stress histories are then "corrected" for plasticity using the Neuber[8]
equal energy method. Finally these plasticity corrected stresses and strains are
placed in an overall local hysteresis loop [10] and fatigue damage is
computed given the maximum and minimum stress-strain of the tips of each hysteresis
loop set.

A process similar to the above is used by all of the commercial and
private company fatigue crack initiation prediction software packages available today.
In the following sections two variations of this process are described in
greater detail. The first is a simplification of the overall process which
allows an analyst to make a calculation for a few load cases and a few elements.
The second method can handle many load channels (vectors) applied to a component
or vehicle body, and through the use of elastic load/stress superposition and
some multiaxial stress simplifications, is used to compute initiation life for
many thousands of finite elements.

Case 1: The Simplified Method

Fig.1: Simple Durability Analysis using Finite Element Results

When a component or structure carries load cases that are simple enough for
the engineer to extract a few critical loading events, the following process, as
conceptualized in Fig.1, can be applied to predict fatigue life: Note: The following is not the best method to solve this problem, but more a
method of historical interest, which has been applied when computer resources
were limited.

Select the critical load sets that require analysis and run each condition
in an elastic finite element analysis. The selector should be aware of any
phase shift or non-proportionality in the load applications on the proving
ground or service. Some loads could have a cancelling effect if applied
simultaneously, or be additive, in terms of element stress, when applied out
of phase, etc. With additional load channels added to a component model this
load case selection process becomes quite difficult, and at this point the
decision needs to be made to perhaps switch to the more complex multi-load
channel method described in Case_2 below.

Measure or calculate the time history of each of the load vectors in
service usage or proving ground; -or whatever the expected loading events
are to be. Typically such histories are recorded on data logging devices
as a prototype or similar vehicle is subjected to a sample of the expected events.
Each load history can then be cycle counted,
( An example of such a counting program is available
here. )
There are several variations of programs that rainflow count on the internet.
The one shown above is base on the push-down list material memory model program
in ref.[5]. Another commonly used program is ref. [6].
The results of the counting process can be placed into a
SAE Standard J2623_200204 Rainflow file format example. or
here.
Refer to
SAE Standard J2623_200204 for details.

A traditional Level Crossing Count can also be made and plotted
(using the program:
lcross.f ).

The Rainflow counting method is however generally preferred for better accuracy
of cycles counted, and is the suggested history input method for many of the
sample calculators available on this web site.

Note: It is good practice to numerically sort the data lines of the rainflow
output file by largest Range first, if the routine does not do so
automatically. The largest stress ranges usually cause much of the fatigue damage
and are best displayed at the top of the data lines.

From your plots and examination of the important load history Rainflow
count tables select the Rainflow files you feel are most critical to your
design. The loads of the Rainflow files should then be scaled into the
von Mises (or other) stress for the elements you feel are important.

Obtain the cyclic axial fatigue data set for your material of interest.
In the example above clicking on the "AA 7075-T6 (Endo/Morrow)"
will return a typical data set in SAE Standard No. J2409_200411 data file format.
The creation of a Fitted curve
for use by one of the calculators is a simple process and will be the
subject of a further web page.

Run a fatigue calculation.
For now, in the learning stage, the reader is advised to
click on the Calculator link, as in the above example, and fill in some of
the critical max and min elastic stresses for an element. Then click on
calculate. The page returned will show a table of the predicted lives for various
damage parameters and a stress-strain plot of the expected local stresses and
strains after application of the Neuber plasticity correction. A cummulative plot
of the rainflow cycles and their expected fatigue damage is shown below the
local stress-strain plot.